On interpolative Hardy-Rogers type cyclic contractions

Authors

DOI:

https://doi.org/10.4995/agt.2024.19885

Keywords:

Hardy-Rogers, interpolation, fixed point, metric space

Abstract

Recently, Karapınar introduced a new Hardy-Rogers type contractive mapping using the concept of interpolation and proved a fixed point theorem in complete metric space. This new type of mapping, called "interpolative Hardy-Rogers type contractive mapping" is a generalization of Hardy-Rogers's fixed point theorem. Following this direction of research, in this paper, we will present some fixed point results of Hardy-Rogers-type for cyclic mappings on complete metric spaces. Moreover, an example is given to illustrate the usability of the obtained results.

Downloads

Download data is not yet available.

Author Biographies

Mohamed Edraoui, University of Hassan II Casablanca

Laboratory of Analysis, Modeling, and Simulation, Department of Mathematics and Computer Sciences, Ben M’Sik Faculty of Sciences

Amine El koufi, Université Ibn-Tofail

High School of Technology ; Lab of PDE’s, Algebra and spectral geometry, Faculty of Sciences

Mohamed Aamri, University of Hassan II Casablanca

Laboratory of Algebra, Analysis and Applications, Department of Mathematics and Computer Sciences, Ben M’Sik Faculty of Sciences

References

M. A. Al-Thafai, and N. Shahzad, Convergence and existence for best proximity points, Nonlinear Analysis 70 (2009), 3665-3671. https://doi.org/10.1016/j.na.2008.07.022

H. Aydi, E. Karapınar, and A. F. Roldán López de Hierro, w-interpolative Cirić-Reich-Rus-type contractions, Mathematics 7, no. 1 (2019), Paper no. 57. https://doi.org/10.3390/math7010057

M. Edraoui, M. Aamri, and S. Lazaiz, Fixed point theorems for set-valued Caristi type mappings in locally convex space, Adv. Fixed Point Theory 7 (2017), 500-511.

M. Edraoui, M. Aamri, and S. Lazaiz, Fixed point theorem for α-nonexpansive wrt orbits in locally convex space, J. Math. Comput. Sci. 10 (2020), 1582-1589.

M. Edraoui, A. El koufi, and S. Semami, Fixed points results for various types of interpolative cyclic contraction, Appl. Gen. Topol. 24, no. 2 (2023), 247-252. https://doi.org/10.4995/agt.2023.19515

Y. El Bekri, M. Edraoui, J. Mouline, A. Bassou, Interpolative Cirić-Reich-Rus-type contraction in G-metric spaces, Journal of Survey in Fisheries Sciences 10, no. 3 (2023), 17-20.

Y. El Bekri, M. Edraoui, J. Mouline, and A. Bassou, Cyclic coupled fixed point via interpolative Kannan type contractions, Mathematical Statistician and Engineering Applications 72, no. 2 (2023), Paper no. 24.

Y. U. Gaba, and E. Karapınar, A new approach to the interpolative contractions, Axioms 8 (2019), Paper no. 110. https://doi.org/10.3390/axioms8040110

G. E. Hardy, and T. D. Rogers, A generalization of a fixed point theorem of Reich, Can. Math. Bull. 16 (1973), 201-206. https://doi.org/10.4153/CMB-1973-036-0

R. Kannan, Some results on fixed points. II, Am. Math. Mon. 76 (1969), 405-408. https://doi.org/10.1080/00029890.1969.12000228

E. Karapınar, Revisiting the Kannan type contractions via interpolation, Adv. Theory Nonlinear Anal. Appl. 2, no. 2 (2018), 85-87. https://doi.org/10.31197/atnaa.431135

E. Karapınar, Interpolative Kannan-Meir-Keeler type contraction, Advances in the Theory of Nonlinear Analysis and its Application 5, no. 4 (2011), 611-614. https://doi.org/10.31197/atnaa.989389

E. Karapınar, A survey on interpolative and hybrid contractions, In: Mathematical Analysis in Interdisciplinary Research 179, Springer International Publishing (2019), 431-475. https://doi.org/10.1007/978-3-030-84721-0_20

E. Karapınar, R. Agarwal, and H. Aydi, Interpolative Reich-Rus-Cirić type contractions on partial metric spaces, Mathematics 6, no. 11 (2018), Paper no. 256. https://doi.org/10.3390/math6110256

E. Karapınar, A. Alid, A. Hussain, and H. Aydi, On interpolative Hardy-Rogers type multivalued contractions via a simulation function, Filomat 36, no. 8 (2022), 2847-2856. https://doi.org/10.2298/FIL2208847K

E. Karapınar, O. Alqahtani, and H. Aydi, On interpolative Hardy-Rogers type contractions, Symmetry 11 (2019), Paper no. 8. https://doi.org/10.3390/sym11010008

E. Karapınar, and M. Erhan, Best proximity point on different type contractions, Applied Mathematics & Information Sciences 5, no. 3 (2011) , 558-569.

E. Karapınar, Y. M. Erhan, and A. Y. Ulus, Fixed point theorem for cyclic maps on partial metric spaces, Appl. Math. Inf. Sci. 6 (2012), 239-244. https://doi.org/10.1186/1687-1812-2012-174

E. Karapınar, A. Fulga, and A. F. Roldán López de Hierro, Fixed point theory in the setting of (α,β,ψ,ϕ)-interpolative contractions, Adv. Differ. Equations (2021), Paper no. 339. https://doi.org/10.1186/s13662-021-03491-w

E. Karapınar, A. Fulga, and S. S. Yeşilkaya, Interpolative Meir-Keeler Mappings in modular metric spaces, Mathematics 10, no. 16 (2022), Paper no. 2986. https://doi.org/10.3390/math10162986

E. Karapınar, A. Fulga, and S. S. Yeşilkaya, New results on Perov-interpolative contractions of Suzuki type mappings, J. Funct. Spaces (2021), Art. ID 9587604. https://doi.org/10.1155/2021/9587604

E. Karpagam, and S. Agrawal, Best proximity point theorems for cyclic orbital Meir-Keeler contraction maps, Nonlinear Analysis 74, no. 4 (2011), 1040-1046. https://doi.org/10.1016/j.na.2010.07.026

M. S. Khan, Y. M. Singh, and E. Karapınar, On the interpolative (ϕ,ψ)-type Z-contraction, UPB Sci. Bull. Ser. A 83 (2021), 25-38.

W. A. Kirk, P. S. Srinivasan, and P. Veeramani, Fixed point for mappings satisfying cyclical contractive conditions, Fixed Point Theory 4 (2003), 79-89.

E. Mohamed, A. Mohamed, and L. Samih, Relatively cyclic and noncyclic P-contractions in locally K-convex space, Axioms 8 (2019), Paper no. 96. https://doi.org/10.3390/axioms8030096

Sh. Rezapour, M. Derafshpour, and N. Shahzad, Best proximity point of cyclic φ-contractions in ordered metric spaces, Topological Methods in Nonlinear Analysis, to appear.

K. Safeer, and R. Ali, Interpolative contractive results for m-metric spaces, Ad.n the Theory of Nonlinear Analysis and its App. 7, no. 2 (2023), 336-347. https://doi.org/10.31197/atnaa.1220114

S. S. Yeşilkaya, C. Aydin, and Y. Aslan, A study on some multi-valued interpolative contractions, Communications in Advanced Mathematical Sciences 3, no. 4 (2020), 208-217. https://doi.org/10.33434/cams.794172

Downloads

Published

2024-04-02

How to Cite

[1]
M. Edraoui, A. El koufi, and M. Aamri, “On interpolative Hardy-Rogers type cyclic contractions”, Appl. Gen. Topol., vol. 25, no. 1, pp. 117–124, Apr. 2024.

Issue

Section

Regular Articles